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The Darboux integral, also called a Darboux-Stieltjes integral, is a variant of the Stieltjes integral that is defined as a common value for the lower and upper Darboux ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

The Darboux cubic Z(X_(20)) of a triangle DeltaABC is the locus of all pedal-cevian points (i.e., of all points whose pedal triangle is perspective with DeltaABC). It is a ...

The rotation vector of the trihedron of a curve with curvature kappa!=0 when a point moves along a curve with unit speed. It is given by D=tauT+kappaB, (1) where tau is the ...

Darboux's formula is a theorem on the expansion of functions in infinite series and essentially consists of integration by parts on a specific integrand product of functions. ...

The partial differential equation u_(xy)+(alphau_x-betau_y)/(x-y)=0.

sum_(k=0)^m(phi_k(x)phi_k(y))/(gamma_k)=(phi_(m+1)(x)phi_m(y)-phi_m(x)phi_(m+1)(y))/(a_mgamma_m(x-y),) (1) where phi_k(x) are orthogonal polynomials with weighting function ...

For three consecutive orders of an orthonormal polynomial, the following relationship holds for n=2, 3, ...: p_n(x)=(A_nx+B_n)p_(n-1)(x)-C_np_(n-2)(x), (1) where A_n>0, B_n, ...

The partial differential equation u_(xy)+(N(u_x+u_y))/(x+y)=0.

A type of integral which is an extension of both the Riemann integral and the Lebesgue integral. The original Denjoy integral is now called a Denjoy integral "in the ...